Mainly because winding down airline business will turn it into a sudden and from there on increasing loss. Airline operation nowadays is calculated in most cases toward a rather high plane utilization. Even more so on low cost enterprises. Sometimes even 10% less passengers may turn a profitable flight into a loss.
Airlines depend on filling up flights - until the last seat and last moment (last minute bookings being, depending on the business plan, even being more profitable). As soon as an airline would announce the intention to close down, new bookings will dry up quick, making next to every flight after this unprofitable.
This all is due the fact that, unlike a brick and mortar store, most cost of an airline are operational cost. There is no valuable inventory to be sold of over time, or much existing machinery to be run until the last moment to convert existing materials in (somewhat) higher valuable products, to turn it into cash. For Airlines there is none (No, collector value of in flight magazines don't really count), so shuting down the flights removes next to all further expenses, stoping any further increase of debt.
Not to mention, that flying after such an announcement would become almost impossible as each and every supplier would demand cash payment from that moment on - with airport fees and fuel payment most prominent - something a money strapped airline hardly can provide. Airlines that tried to go that way usually postponed the shutdown just by days - and often with planes stuck in all corners of the world, unable to return, not able to sell them, but instead adding more debt in airport parking fees.